It was easy to understand why as his side struggled to overcome part-time opponents at Ibrox for the second time in the space of eight days.
How, you have to wonder, would they have fared if the Scotland internationalist, their star performer, had not been present in their starting line-up? Yes, being reduced to 10 men in the second half after centre- half Bilel Mohsni was stupidly ordered off for a second bookable offence hindered their cause.
Yet they were still highly fortunate to edge out opponents who for long spells towards the end of an enthralling match were the superior side. Without Wallace, who collected the Man of the Match award after another fine display, it is not inconceivable they could have been held to a draw or even suffered a defeat.
The narrow victory maintained the 23-point lead that Rangers have over Dunfermline at the top of the SPFL League One table. But their performance once again left a great deal to be desired and they left the field with the jeers of those supporters still left inside the stadium ringing in their ears.
David Templeton, who had performed so well after coming on as a substitute in his side's last two games against Forfar Athletic and Arbroath, came in to the Rangers starting line-up.
It was the first time in nearly two months that Templeton had been on the field as his side kicked off a game. Injuries and a loss of form have curtailed his involvement. However, he more than merited his place in the side given the excellence of his all-round play and his two well-taken goals against both Forfar and Arbroath last month.
The 25-year-old seemed to energise a team that has, possibly as a result of their sizeable lead at the top of the table, grown decidedly flat in recent weeks. He should have put Rangers in front in the third minute when Dean Shiels supplied him with the ball with a precise cut-back, but he shot straight at Graeme Smith.
The presence of Shiels, who played just off lone striker Jon Daly in a 4-4-1-1 formation, also seemed to have a positive influence on his side's performance levels. Like Templeton, the Northern Ireland internationalist has not featured much for Rangers in this campaign due to a lack of fitness and form.
The player, though, is a man reborn these days and he opened the scoring with a fine piece of skill in the 13th minute. Despite the close attentions of Brechin defender Paul McLean, Shiels managed to tee the ball up and then curl a left foot shot into the top left corner. It was the perfect way for him to mark his 29th birthday.
Having been involved so infrequently in the first team, Shiels had been the subject of some enquiries during the transfer window from clubs looking to take him on loan. McCoist will also have been pleased that he managed to retain his services given how important he was to this triumph.
Daly built on the lead in the 25th minute in less spectacular fashion after his side was awarded a free kick on the right flank by referee Stevie O'Reilly. Wallace whipped the ball into the Brechin six-yard box and his team-mate rose and diverted the ball into the net with a glancing downward header, taking his tally for the season to 20.
As the teams trudged off at half-time, it looked as if there would only be one winner. But Brechin netted early in the second half. Cammy Bell had no chance with the 25-yard shot from Steven Robb in the 52nd minute.
That strike gave the visitors hope they could snatch a result. Their cause was helped when Rangers centre-half Mohsni was sent off in the 61st minute after kicking a ball at Allan Walker. McCoist immediately replaced Shiels with right-back Richard Foster and moved Sebastien Faure to his favoured position at centre-half to protect their slender lead.
Templeton should really have scored after some outstanding work by Nicky Law in the 74th minute. With an empty net gaping invitingly, he ballooned his shot over the bar. Brechin had their chances too in what were fraught closing stages for Rangers. The home team were lucky to collect all three points at the end of the 90 minutes.